If r varies directly as t andr= -20 when t = 4, find r when t= -6.

Stolb23 [73]

To find the area of a rhombus using diagonals, you must multiple the diagonals and divide then by 2. In this case 37 * 20 is 740. 740/2 is 370. 370 is your answer

5 0

3 years ago

Geometry help please? 4 questions. Thanks!

wel

Question 1:

Statement Reasons
m∠ABD + m∠DBC = m∠ABC Angle addition postulate
60° + 40° = m∠ABC Substitution Property of equality
100° = m∠ABC Simplpifying
∠ABC is an obtuse angle Definition of obtuse angle

----------------------------------------------------------------------------------------------------------------

Question 2:

Statement Reasons
AC = BD Given
AC = BC + BD Segment addition postulate
AB + BC = BC + CD Addition property of equality

----------------------------------------------------------------------------------------------------------------

Question 3:

Angle congruence postulate

---------------------------------------------------------------------------------------------------------------

Question 4:

Segment congruence postulate

7 0

3 years ago

The landscaper pours 200 gallons of herbicide in a pond. The herbicide degrades 10% each week. How much will be in the pond afte

weeeeeb [17]

Answer:

180 gallons

Step-by-step explanation:

200 gal

10% = .10

200 x .10 = 20

200 - 20 = 180

5 0

3 years ago

Read 2 more answers

The longest side of a triangle is 3 in. longer than the shortest side. The medium side is 2 in. longer than the shortest side. I

Olenka [21]

s = length of the shortest side of the triangle

m = length of the medium side of the triangle

l = length of the longest side of the triangle

(you can use different variables like l, w, h, x, y.......)

Perimeter(P) of a triangle is the total sum of the sides, in this case:

P = s + m + l

You know:

P = 26in

l = s + 3 [longest side is 3in longer/more than(addition) the shortest side]

m = s + 2 [medium side is 2in longer than the shortest side]

To find the lengths of the three sides, you can do this:

P = s + m + l Substitute/plug in what you know. So plug in 26 into "P" since P = 26, plug in (s + 3) into "l" since l = s + 3, and plug in (s + 2) into "m" since m = s + 2

26 = s + (s + 2) + (s + 3) Combine like terms (like terms have the same variable and power/exponent)

26 = 3s + 5 To find "s", isolate/get the variable "s" by itself. Subtract 5 on both sides

21 = 3s Divide 3 on both sides to get "s" by itself

7 = s

Now that you found s, you can use it to find the other sides

m = s + 2 Substitute/plug in 7 into "s" since s = 7

m = 7 + 2

m = 9

l = s + 3 Plug in 7 into "s"

l = 7 + 3

l = 10

The longest side is 10 inches, the medium side is 9 inches, the shortest side is 7 inches

PROOF

P = s + m + l

P = 7 + 9 + 10

P = 26 inches

7 0

3 years ago

Read 2 more answers

The average American man consumes 9.8 grams of sodium each day. Suppose that the sodium consumption of American men is normally

Alex Ar [27]

Answer:

(a) The distribution of X is N (9.8, 0.8²).

(b) The probability that an American consumes between 8.8 and 9.9 grams of sodium per day is 0.4461.

(c) The middle 30% of American men consume between 9.5 grams to 10.1 grams of sodium.

Step-by-step explanation:

The random variable X is defined as the amount of sodium consumed.

The random variable X has an average value of, μ = 9.8 grams.

The standard deviation of X is, σ = 0.8 grams.

(a)

It is provided that the sodium consumption of American men is normally distributed.

The random variable X follows a normal distribution with parameters μ = 9.8 grams and σ = 0.8 grams.

Thus, the distribution of X is N (9.8, 0.8²).

(b)

If X ~ N (µ, σ²), then $Z=\frac{X-\mu}{\sigma}$ , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z ~ N (0, 1).

To compute the probability of Normal distribution it is better to first convert the raw score (X) to z-scores.

Compute the probability that an American consumes between 8.8 and 9.9 grams of sodium per day as follows:

$P(8.8$

$=P(-1.25$

Thus, the probability that an American consumes between 8.8 and 9.9 grams of sodium per day is 0.4461.

(c)

The probability representing the middle 30% of American men consuming sodium between two weights is:

$P(x_{1}$

Compute the value of z as follows:

$P(-z$

The value of z for P (Z < z) = 0.65 is 0.39.

Compute the value of x₁ and x₂ as follows:

$-z=\frac{x_{1}-\mu}{\sigma}\\-0.39=\frac{x_{1}-9.8}{0.8}\\x_{1}=9.8-(0.39\times 0.8)\\x_{1}=9.488\\x_{1}\approx9.5$ $z=\frac{x_{2}-\mu}{\sigma}\\0.39=\frac{x_{1}-9.8}{0.8}\\x_{1}=9.8+(0.39\times 0.8)\\x_{1}=10.112\\x_{1}\approx10.1$

Thus, the middle 30% of American men consume between 9.5 grams to 10.1 grams of sodium.

4 0

3 years ago